data_fun <- function(N_bin1 = 10, N_bin3 = 5){
  
  T <- 72 # for count data
  
  # ZEROS TRICK
  zeros <- rep(0,T)
  Up2 <- 4000
  Up4 <- 6000
  
  # HMM
  # N_max1 = 79
  # N_max3 = 49
  sc = 1 #100
  
  # # BINS for approximative HMM INTERGRATION
  # N_bin1 = 59 # 109 #59 #  # reduction to be based on Gamma plots
  # bin_size1 = 49 #29 # 69#  odd so the midpoints are integer
  # N_bin3 = 49 #  # reduction to be based on Gamma plots 
  # bin_size3 = 19#  odd so the midpoints are integer
  # 
  # N_bin_min1 = 12 # how many first bins are skipped 
  # N_bin_min3 = 20 # how many first bins are skipped
  
  
  # Number of quantiles for approximative HMM INTERGRATION
#   N_bin1 = 10 # Number of intervals
  # Lower bin values:
  qu1 <- c(0:(N_bin1-1))/N_bin1
  mid1 <- qu1+qu1[2]/2
  
#   N_bin3 = 5 # Number of intervals
  # Lower bin values:
  qu3 <- c(0:(N_bin3-1))/N_bin3
  mid3 <- qu3+qu3[2]/2
  
  
  # Ring-recovery data:
  ring1 <- 43
  
  m1 <- matrix(c(
    348, 33, 5, 0, 0, 3, 4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    141,  0,17, 6, 4, 2, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    265,  0, 0,31,12, 2, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    80,   0, 0, 0,12, 3, 2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    335,  0, 0, 0, 0,34,22, 7, 7, 1, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    98,   0, 0, 0, 0, 0, 5, 6, 4, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    170,  0, 0, 0, 0, 0, 0,23, 7, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    115,  0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    45,   0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    117,  0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    137,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 1, 1, 0, 0, 1, 0, 0, 0, 3, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    131,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 9, 3, 1, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    371,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,32, 9, 5, 4, 1, 2, 1, 0, 2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    379,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,35, 11, 2,  0,  4,  0,  2, 1, 1, 0,  0, 0,  0,  0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0, 0, 0, 0, 0, 0, 0,
    503,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 18,  6,  0,  0,  1, 2, 0, 3,  0, 0,  0,  0, 0, 0, 1, 0, 1,  0, 0,  0,  0, 0, 0, 0, 0, 0, 0, 0,
    476,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0, 39, 16,  8,  6,  3, 3, 2, 3,  1, 2,  0,  0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0, 0, 0, 0, 0, 0, 0,
    446,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0, 31, 17,  4,  6, 1, 2, 0,  0, 0,  0,  0, 0, 0, 0, 0, 2,  0, 0,  0,  0, 0, 1, 0, 0, 0, 0, 0,
    282,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0, 23, 14,  4, 0, 1, 1,  0, 0,  2,  0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0, 0, 0, 0, 0, 0, 0,
    236,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0, 32,  5, 4, 2, 0,  0, 1,  0,  1, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0, 0, 0, 0, 0, 0, 0,
    282,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0, 10, 0, 6, 2,  0, 1,  1,  0, 0, 1, 0, 0, 0,  0, 0,  0,  0, 0, 0, 0, 0, 0, 0, 0,
    450,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0,30, 7, 3,  0, 1,  0,  0, 1, 1, 0, 1, 0,  0, 0,  1,  0, 0, 0, 0, 0, 0, 0, 0,
    589,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0,49, 7,  4, 1,  1,  0, 1, 1, 0, 0, 0,  0, 0,  1,  0, 0, 0, 0, 0, 0, 0, 0,
    464,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0,33, 13, 5,  2,  1, 1, 0, 0, 0, 0,  0, 0,  1,  0, 0, 0, 0, 0, 0, 1, 0,
    237,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0, 20, 4,  0,  2, 2, 0, 0, 0, 0,  2, 0,  0,  0, 0, 0, 0, 0, 0, 0, 0,
    434,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0, 32,13, 12, 0, 2, 4, 1, 0,  0, 0,  0,  0, 0, 0, 1, 1, 0, 0, 0,
    648,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0,35, 13, 7, 0, 2, 1, 0,  1, 0,  0,  0, 0, 0, 0, 0, 0, 1, 0, 
    740,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0, 44, 5, 6, 1, 0, 0,  0, 0,  1,  0, 0, 2, 0, 0, 0, 0, 0, 
    1014, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0,41,11, 3, 5, 5,  5, 1,  0,  1, 2, 0, 0, 1, 0, 1, 0, 
    777,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0, 0,30, 6, 7, 1,  2, 3,  1,  1, 0, 0, 1, 0, 0, 0, 0,  
    1110, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0, 0, 0,59,22, 9,  1, 1,  0,  0, 1, 1, 0, 1, 0, 1, 0,  
    814,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0, 0, 0, 0,50,10,  2, 3,  0,  0, 3, 0, 1, 1, 0, 0, 0,  
    732,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0, 0, 0, 0, 0,24, 11, 2,  3,  2, 1, 0, 0, 1, 0, 0, 0, 
    578,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0, 0, 0, 0, 0, 0, 20, 6,  3,  3, 3, 1, 0, 0, 1, 1, 1,  
    498,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0, 0, 0, 0, 0, 0,  0,11,  8,  5, 2, 2, 0, 1, 1, 0, 1, 
    527,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0, 0, 0, 0, 0, 0,  0, 0, 18, 12, 1, 4, 2, 1, 3, 0, 2, 
    596,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0, 0, 0, 0, 0, 0,  0, 0,  0, 28, 5, 2, 3, 0, 2, 0, 0,
    492,	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0, 0, 0, 0, 0, 0,  0, 0,  0,  0,10, 6, 3, 0, 1, 1, 0,
    565,	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0,21, 2, 0, 0, 0, 1,
    572,	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0, 0,26, 5, 2, 1, 1,
    576,	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0, 0, 0,20, 6, 3, 1,
    683,	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0, 0, 0, 0,23, 5, 2,
    510,	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0, 0, 0, 0, 0,16, 0,
    718,	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 0, 0, 0,  0,  0, 0,  0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0, 0, 0, 0, 0, 0,18), 
    nrow=43,ncol=44,byrow=T)  
  
   
  m <- cbind(m1[,2:(ring1+1)],m1[,1]-rowSums(m1[,2:(ring1+1)]))
  m[,(ring1+1)] = round(m[,(ring1+1)]/sc)
  rel <- rowSums(m)
  
  
  # Count data:
  y <- round(c(0,4000, 3500, 3850, 4050, 4000, 4075, 4150, 4150, 4375, 4500, 4800, 4700, 3650, 3550, 3400, 3850, 4300, 
         4075, 4125, 2700, 2800, 3575, 4100, 4550, 4700, 4575, 4800, 4425, 4150, 4500, 4075, 4550, 4350, 4675,
         3700, 2250, 2450, 2825, 2925, 3225, 3725, 3925, 4125, 4575, 4625, 4925, 5175, 5100, 5075, 5125, 5375, 
         5200, 5575, 5675, 5350, 5425, 5700, 5775, 5109, 5166, 5637, 5898, 6143, 5936, 6051, 6310, 6447, 6950, 
         6570, 6653, 6940)/sc)
  
  
  # Starting in T=1 = 1927
  # T=2 = first year of count data (1928)
  # T=28 = first year of ring-recovery data (1955)
  fdays <- c(12, 26, 2, 9, 6, 8, 3, 2, 17, 3, 4, 8, 38, 12, 30, 3, 2, 15, 18, 46, 6,  
             3, 6, 15, 6, 13, 17, 22, 22, 4, 11, 9, 2, 1, 22, 57, 12, 13, 13, 2, 15, 
             13, 20, 12, 3, 1, 5, 0, 6, 9, 11, 33, 7, 2, 27, 5, 7, 25, 30, 16, 3, 1,  
             1, 12, 12, 9, 6, 3, 18, 10, 0, 1)
  
  # Normalise fdays:
  f <- (fdays-mean(fdays))/sd(fdays)
  
  # Time (for recovery probability regression) - normalised.
  # time <- c(1:T)
  time <- c(1:ring1)
  time <- (time-mean(time))/sd(time)
  
  data <- list(y=y,T=T,m=m,ring1=ring1,f=f,time=time,rel=rel, zeros=zeros, Up2=Up2, Up4=Up4, 
               N_bin1=N_bin1, N_bin3=N_bin3, mid1=mid1, mid3=mid3)

  
}